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Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors. [video] Retrieved from https://doi.org/doi:10.7282/T3DR2TFX

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TitleEarly algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors.
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1996-03-13
Persistent URLhttps://doi.org/doi:10.7282/T3DR2TFX
DescriptionIn the ninth clip in a series of ten from the fifth of seven interviews, 8th grader Stephanie continues her exploration of Early Algebraic Ideas about Binomial Expansion. Researcher Carolyn Maher refers to written work that Stephanie had completed in an earlier interview where she had recorded the binomial (a + b) expanded to successive powers from one to five. Stephanie maps the coefficients for each expansion to the corresponding row of Pascal's Triangle and recognizes that there is also a correspondence to unifix towers built to the same height, when selecting from two colors. She then provides an explanation of the correspondence between particular terms in one of the expansions with the corresponding unifix-cube towers.
The problems as presented to Stephanie:
Compare the coefficients from successive powers of the binomial expansion to the rows of Pascal's Triangle.
Can the various terms of any given power of the expansion be shown to correspond to towers of different heights, selecting from two colors?
Math ToolColor markers
Math StrandAlgebra
Math ProblemTowers, Binomial expansion, Explore Pascal's triangle
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Constructing a pictorial model, Referencing a previous problem, Recognizing a pattern, Recognizing an isomorphism
Grade Level8
Student ParticipantsStephanie (student)
MediatorsMaher, Carolyn Alexander (Researcher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingInformal learning
Student GenderFemale
Student EthnicityWhite
Camera ViewsWork view, Student view
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Date Captured1996-03-13
Local IdentifierA68A69-ALG-BIEX-CLIP009
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas about binomial expansion, Stephanie's interview five of seven, Clip 9 of 10: Relating coefficients of the binomial expansion to Pascal's Triangle and to unifix cube towers, selecting from two colors.
   Date: 2011
   Author: Aboelnaga, Eman Y. (Eman Yousry) (Rutgers, the State University of New Jersey)

   Name: A case study: the development of Stephanie's algebraic reasoning
   Reference: http://hdl.rutgers.edu/1782.1/rucore10001500001.ETD.000057485
Source
   Title: A68, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (student view), Grade 8, March 13, 1996, raw footage.
   Identifier: A68-19960313-KNWH-SV-INT-GR8-ALG-BIEX-RAW
Source
   Title: A69, Early algebra ideas about binomial expansion, Stephanie's interview five of seven (work view), Grade 8, March 13, 1996, raw footage.
   Identifier: A69-19960313-KNWH-WV-INT-GR8-ALG-BIEX-RAW